Added compression parts

Advanced/Compression/parts/0 intro.tex

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+\section{Introduction}
+
+\definition{}
+An \textit{alphabet} is a set of symbols. Two examples are
+$\{\texttt{A}, \texttt{B}, \texttt{C}, \texttt{D}\}$ and $\{\texttt{0}, \texttt{1}\}$.
+
+\definition{}
+A \textit{string} is a sequence of symbols from an alphabet. \par
+For example, \texttt{CBCAADDD} is a string over the alphabet $\{\texttt{A}, \texttt{B}, \texttt{C}, \texttt{D}\}$.
+
+\problem{}
+Say we want to store a length-$n$ string over the alphabet $\{\texttt{A}, \texttt{B}, \texttt{C}, \texttt{D}\}$ as a binary blob. \par
+How many bits will we need? \par
+\hint{
+	Our alphabet has four symbols, so we can encode each symbol using two bits, \par
+	mapping $\texttt{A} \rightarrow \texttt{00}$,
+	$\texttt{B} \rightarrow \texttt{01}$,
+	$\texttt{C} \rightarrow \texttt{10}$, and
+	$\texttt{D} \rightarrow \texttt{11}$.
+}
+
+\begin{solution}
+	$2n$ bits.
+\end{solution}
+
+\vfill
+
+
+\problem{}<naivelen>
+Similarly, we can use a na\"ive coding scheme to encode an $n$-symbol string over an alphabet of size $k$ \par
+using $n \times \lceil \log_2k \rceil$ bits. Convince yourself that this is true.
+
+
+\vfill
+Of course, this isn't ideal---we can do much better than $n \times \lceil \log_2k \rceil$.
+We will spend the rest of this handout exploring more efficient ways of encoding such sequences of symbols.
+\pagebreak